By default, Plex will try to authenticate users that connect to your server using the Plex API servers. This prevents outside users from being able to just connect to the server and browse everything. Even if remote access is off, it still uses authentication to verify who is “allowed” to view your server’s content.
If you want to disable that, you can. You need to tell each client to allow “insecure connections”. This means that if authentication cannot be done, they may try to connect to the server anyway. Next, you need to specifically tell the server itself which computers (or networks) are allowed to connect “insecurely” to it if it can’t authenticate.
All this needs to be done with an internet connection in the first place (so I hear) but once done Plex can run entirely without internet from then on. Adding of new media may need to retrieve metadata for those media depending on server settings/libraries, but otherwise can be used offline if you don’t care for metadata (file names, descriptions, etc).